Drain and rinse the soaked chickpeas. Pat them dry with a paper towel.
In a food processor, combine the chickpeas, onion, garlic, parsley, and cilantro. Pulse until the mixture is finely ground but not pureed. The mixture should be slightly coarse.
Add the ground cumin, ground coriander, baking powder, salt, black pepper, and cayenne pepper (if using). Pulse a few more times to combine.
Transfer the mixture to a bowl, cover, and refrigerate for at least 1 hour to allow the flavors to meld and the mixture to firm up.
Heat about 2 inches (5 cm) of vegetable oil in a deep pan or skillet over medium heat.
Using your hands or a falafel scoop, form the mixture into small balls or patties (about 1 inch / 2.5 cm in diameter).
Carefully drop the falafel into the hot oil, a few at a time, being careful not to overcrowd the pan. Fry until golden brown and crispy, about 4-5 minutes, turning occasionally.
Remove the falafel from the oil with a slotted spoon and drain on paper towels.
Enjoy your meal!